Counterpart Theory

This paper argues that a counterpart-theoretic treatment of events, combined with a counterfactual theory of causation, can help resolve three puzzles from the causation literature. First, CCT traces the apparent contextual shifts in our causal attributions to shifts in the counterpart relation which obtains in those contexts. Second, being sensitive to shifts in the counterpart relation can help diagnose what goes wrong in certain prominent examples where the transitivity of causation appears to fail. Third, CCT can help us resurrect the (...) much-maligned fragility response to the problems of late pre-emption by understanding fragility in counterpart-theoretic terms. Some reasons to prefer this CCT approach to rivals are discussed. (shrink)

This paper investigates the form a modal realist analysis of possibility and necessity should take. It concludes that according to the best version of modal realism, the notion of a world plays no role in the analysis of modal claims. All contingent claims contain some de re element; the effect of modal operators on these elements is described by a counterpart theory which takes the same form whether the de re reference is to a world or to something else. This (...) fully general counterpart theory can validate orthodox modal logic, including the logic of 'actually'. (shrink)

A new puzzle about material constitution is presented and its implications are discussed. The moral of the story is that familiar intuitions supporting a neo-Aristotelian view of the material world are contradictory. To accommodate these intuitions is to embrace inconsistency. Therefore, neo-Aristotelianism is worse off for its intuitive appeal. Furthermore, the puzzle is used to argue for an account of ordinary modal thought and language that’s reconstructive, or ameliorative.

David Lewis argues at length against haecceitism and goes as far as claiming that, on a certain counterpart-theoretic construal, the doctrine is unintelligible or inconsistent. I argue, contra Lewis, that both qualitative and non-qualitative counterpart theory are in fact committed to haecceitism, but that this commitment is harmless since what is really at stake for a counterpart theorist such as Lewis are more general supervenience claims that are independent of haecceitism. I further argue that Lewis's formulation of the doctrine suffers (...) from two important defects that, once remedied, free counterpart theory of its haecceitistic commitments. Along the way I discuss an objection to the effect that the cheap substitute is inconsistent in the presence of an 'actually' operator. This paper therefore brings together important critical discussion on haecceitism and counterpart theory. (shrink)

Standard accounts of counterfactuals with metaphysically impossible antecedents take them to by trivially true. But recent work shows that nontrivial countermetaphysicals are frequently appealed to in scientific modeling and are indispensable for a number of metaphysical projects. I focus on three recent discussions of counterpossible counterfactuals, which apply counterpossibles in both scientific and metaphysical modeling. I show that a sufficiently developed modal counterpart theory can provide a semantics for a wide range of counterpossibles without any inconsistent possibilities or other forms (...) of impossible worlds. But such a view faces problems: in order for the metaphysical views I discuss to bear weight, there must be a significant difference between the metaphysical possibilities and impossibilities. I will show how the counterpart-theoretic view delineates the possible from impossible, while still making room for the impossible. (shrink)

Lewis (1968) claims that his language of Counterpart Theory (CT) interprets modal discourse and he adverts to a translation scheme from the language of Quantifed Modal Logic (QML) to CT. However, everybody now agrees that his original translation scheme does not always work, since it does not always preserve the ‘intuitive’ meaning of the translated QML-formulas. Lewis discusses this problem with regard to the Necessitist Thesis, and I will extend his discourse to the analysis of the Converse Barcan Formula. Everyone (...) also agrees that there are CT-formulas that can express the QMLcontent that gets lost through the translation. The problem is how we arrive to them. In this paper, I propose new translation rules from QML to CT, based on a suggestion by Kaplan. However, I will claim that we cannot have ‘the’ translation scheme from QML to CT. The reason being that de re modal language is ambiguous. Accordingly, there are diferent sorts of QML, depending on how we resolve such ambiguity. Therefore, depending on what sort of QML we intend to translate into CT, we need to use the corresponding translation scheme. This suggests that all the translation problems might just disappear if we do what Lewis did not: begin with a fully worked out QML that tells us how to understand de re modal discourse. (shrink)

ABSTRACT Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Kripke's ‘objectual’ interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these Quinean worries. Yet there remain residual Quinean worries for epistemic modality. Theorists have recently been toying with assignment-shifting treatments of epistemic contexts. On such views an epistemic operator ends up binding all the variables in its scope. One might worry that this yields (...) the undesirable result that any attempt to ‘quantify in’ to an epistemic environment is blocked. If quantifying into the relevant constructions is vacuous, then such views would seem hopelessly misguided and empirically inadequate. But a famous alternative to Kripke's semantics, namely Lewis' counterpart semantics, also faces this worry since it also treats the boxes and diamonds as assignment-shifting devices. As I'll demonstrate, the mere fact that a variable is bound is no obstacle to binding it. This provides a helpful lesson for those modelling de re epistemic contexts with assignment sensitivity, and perhaps leads the way toward the proper treatment of binding in both metaphysical and epistemic contexts: Kripke for metaphysical modality, Lewis for epistemic modality. (shrink)

Although David Lewis advocates a counterpart-theoretic treatment of objects but rejects a parallel treatment of events, many philosophers have — mainly to solve some puzzles within the framework of a Lewisian counterfactual analysis of causation — suggested that the counterpart-theoretic treatment be extended to events. This article argues that we had better not be a counterpart theorist of events as long as we want to remain at all faithful to the counterfactual analysis of causation.

Many explanations rely on identity facts. In this paper, I propose an account of how identity facts explain: roughly, the fact that A is identical to B explains another fact whenever that other fact depends, counterfactually, on A being identical to B. As I show, this account has many virtues. It avoids several problems facing accounts of explanatory identities, and when precisified using structural equations, it can be used to defend interventionist accounts of causation against an objection.

In a recent paper, Brian Rabern suggests a semantics for languages with two kinds of modality, standard Kripkean metaphysical modality as well as epistemic modality. This semantics presents an alternative to two-dimensionalism, which was developed in the last decades. Both Rabern’s semantics and two-dimensionalism are subject to a puzzle that Chalmers and Rabern, 210–224 2014) call the nesting problem. I will investigate how Rabern’s semantics answers this puzzle.

Relativized Metaphysical Modality (RMM: Murray and Wilson, 'Relativized metaphysical modality', Oxford Studies in Metaphysics, 2012; Murray, Perspectives on Modal Metaphysics, 2017) exploits 'two-dimensionalist' resources to metaphysical, rather than epistemological, ends: the second dimension offers perspective-dependence without contingency, diverting attacks on 'Classical' analyses of modals (in effect, analyses validating S5 and the Barcan Formulae). Here, we extend the RMM program in two directions. First, we harvest resources for RMM from Lewis's 1980 'Context--Index' (CI) framework: (a) the ban in CI on binding (...) into context-arguments (akin to Kaplan's 'monstrosity' ban) projects a bright line between perspective-dependence and contingency; and (b) CI-postulated connections among meaning, content, truth, argument-structure, context, and modality collectively generate a 'Generalized Humphrey Problem' for any non-Classical analysis (examples covered include appeals to accessibility, contingent domains, and counterpart relations). Second, we sharpen the tools of RMM-based metaphysical analysis, and extend their domain of coverage across familiar anomalies for Classical modals: we revisit earlier RMM-based bulwarks for S5 (against 'Chisholm's Paradox' for moderate flexibility of essence, and nomological necessitarianism); and we now similarly shore up the Barcan Formulae (against the apparent contingency of existence and nonexistence). (shrink)

David Lewis offers two solutions to the problem of the many, one of which relies on supervaluationism and the other on the notion of “almost-identity” for the most part. In this paper, I argue that Lewis’ other metaphysical views constitute reasons to prefer his second solution to the first one. Specifically, Lewis’ theory of propositions and his counterpart theory give rise to two similar problems of the many, which I call “the problem of many propositions” and “the problem of many (...) counterparts” respectively. While both Lewis’ solutions may solve the problem of the many with respect to objects in the actual world, I argue that only his second solution can solve the problem of many propositions and the problem of many counterparts. Therefore, for anyone who accepts Lewis’ metaphysical views on propositions and counterparts, they should embrace Lewis’ second solution to the problem of the many for the reason of unification. (shrink)

In this paper, I will argue that there is a version of possibilism—inspired by the modal analogue of Kit Fine’s fragmentalism—that can be combined with a weakening of actualism. The reasons for analysing this view, which I call Modal Fragmentalism, are twofold. Firstly, it can enrich our understanding of the actualism/possibilism divide, by showing that, at least in principle, the adoption of possibilia does not correspond to an outright rejection of the actualist intuitions. Secondly, and more specifically, it can enrich (...) our understanding of concretism, by proving that, at least in principle, the idea that objects have properties in an absolute manner is compatible with transworld identity. (shrink)

This book defends a radical new theory of contingency as a physical phenomenon. Drawing on the many-worlds approach to quantum theory and cutting-edge metaphysics and philosophy of science, it argues that quantum theories are best understood as telling us about the space of genuine possibilities, rather than as telling us solely about actuality. When quantum physics is taken seriously in the way first proposed by Hugh Everett III, it provides the resources for a new systematic metaphysical framework encompassing possibility, necessity, (...) actuality, chance, counterfactuals, and a host of related modal notions. -/- Rationalist metaphysicians argue that the metaphysics of modality is strictly prior to any scientific investigation; metaphysics establishes which worlds are possible, and physics merely checks which of these worlds is actual. Naturalistic metaphysicians respond that science may discover new possibilities and new impossibilities. This book's quantum theory of contingency takes naturalistic metaphysics one step further, allowing that science may discover what it is to be possible. As electromagnetism revealed the nature of light, as acoustics revealed the nature of sound, as statistical mechanics revealed the nature of heat, so quantum physics reveals the nature of contingency. (shrink)

An intuitive objection to modal realism is that merely possible worlds and their inhabitants seem to be irrelevant to an analysis of modality. Kripke originally phrased the objection in terms of being concerned about one’s modal properties without being concerned about the properties one’s other-worldly counterparts have. The author assesses this objection in a variety of forms, and then provides his own formulation that does not beg the question against the modal realist. Finally, the author considers two potential answers to (...) the objection so understood and concludes that only one of them has a chance of succeeding. (shrink)

A number of philosophers have recently found it congenial to talk in terms of grounding. Grounding discourse features grounding sentences that are answers to questions about what grounds what. The goal of this article is to explore and defend a counterpart-theoretic interpretation of grounding discourse. We are familiar with David Lewis's applications of the method of counterpart theory to de re modal discourse. Counterpart-theoretic interpretations of de re modal idioms and grounding sentences share similar motivations, mechanisms, and applications. I shall (...) explain my motivations and describe two applications of a counterpart theory for grounding discourse. But, in this article, my main focus is on counterpart-theoretic mechanisms. (shrink)

Bundle theories identify material objects with bundles of properties. On the traditional approach, these are the properties possessed by that material object. That view faces a deep problem: it seems to say that all of an object’s properties are essential to it. Essential bundle theory attempts to overcome this objection, by taking the bundle as a specification of the object’s essential properties only. In this paper, I show that essential bundle theory faces a variant of the objection. To avoid the (...) problem, the theory must accept the contingency of identity. I show how this can be achieved in a coherent and well-motivated way, a way that isn’t available to traditional bundle theories. (shrink)

A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or one could reject the orthodox theory of counterfactuals in favor of a (...) hyperintensional semantics that accommodates non-trivial counterpossibles. In this paper, I argue that none of these approaches can account for all the peculiar features of counteridenticals. Instead, I propose a modified version of Lewis’s counterpart theory, which rejects the necessity of identity, and show that it can explain all the peculiar features of counteridenticals in a satisfactory way. I conclude by defending the plausibility of contingent identity from objections. (shrink)

It is commonly assumed that causation is transitive and in this paper I aim to reconcile this widely-held assumption with apparent evidence to the contrary. I will discuss a familiar approach to certain well-known counterexamples, before introducing a more resistant sort of case of my own. I will then offer a novel solution, based on Yablo’s proportionality principle, that succeeds in even these more resistant cases. There is a catch, however. Either proportionality is a constraint on which causal claims are (...) true, and the solution works, or it is not and causation is not transitive after all. I will argue that the first horn has unacceptable consequences and should be rejected, but that the second horn is less costly than it might initially appear. (shrink)

Expressions typically thought to be rigid designators can refer to distinct individuals in the consequents of counterfactuals. This occurs in counteridenticals, such as “If I were you, I would arrest me”, as well as more ordinary counterfactuals with clearly possible antecedents, like “If I were a police officer, I would arrest me”. I argue that in response we should drop rigidity and deal with de re modal predication using something more flexible, such as counterpart theory.

It follows from David Lewis's counterpart-theoretic analysis of modality and his counterfactual theory of causation that causal claims are relativized to a set of counterpart relations. Call this Shlewis's view. I show how Shlewis's view can provide attractively unified solutions to similar modal and causal puzzles. I then argue that Shlewis's view is better motivated, by his own lights, than the view Lewis actually held, and also better motivated than a similar approach which relativizes causal claims to sets of ‘contrast (...) events’. (shrink)

David Lewis may be regarded as an antiessentialist. The reason is that he is said to believe that individuals do not have essential properties independent of the ways they are represented. According to him, indeed, the properties that are determined to be essential to individuals are a matter of which similarity relations among individuals are salient, and salience, in turn, is a contextual matter also determined to some extent by the ways individuals are represented. Todd Buras argues that the acknowledgment (...) of natural properties in counterpart theoretic ontology affects Lewis’s theory with regard to essentialism. Buras’s reasoning is appealing. He claims that, since natural properties determine the existence of similarity relations among individuals that are salient independent of context, Lewis can no longer be claimed to be an antiessentialist. The aim of this paper is to argue, against Buras, that if counterpart theory was antiessentialist before natural properties were taken into account, then it remains so afterwards. (shrink)

Counterpart theory has many benefits, but few are happy to accept the metaphysical setting in which this account of de re modality was developed by its architect, David Lewis. I argue here that counterpart theory can be made acceptable by the lights of those who repudiate the existence of merely possible objects. To the "ersatz" counterpart theorist I offer two stories: one about the relate of the counterpart relation and one about the relation itself. With these in place, I then (...) defend ersatz counterpart theory from a number of objections that can be found in the literature. (shrink)

It is shown that counterpart theory and the duplication account of intrinsicality —two key pieces of the Lewisian package—are incompatible. In particular, the duplication account yields the result that certain intuitively extrinsic modal properties are intrinsic. Along the way I consider a potentially more general worry concerning certain existential closures of internal relations. One conclusion is that, unless the Lewisian provides an adequate alternative to the duplication account, the reductive nature of their total theory is in jeopardy.

It is widely agreed that properties play causal roles: they capture the causal powers of things. But do properties have their causal roles essentially? David Lewis did not think so. He adhered to the doctrine of quidditism, namely the doctrine that the identity of properties is primitive and that they can trade their causal roles. Quidditism is controversial. But Lewis did not see why he should want to reject it. He knew that he could avoid quidditism on the cheap by (...) treating individuals and properties alike in rejecting transworld multilocation of properties and endorsing a counterpart theory for properties. But he did not see why he should want to do so. In this article, I argue that Lewis should have wanted to endorse a counterpart theory for properties in order to reject quidditism. My argument concerns resemblance relations among properties. Another constitutive role of properties is that they capture objective resemblances between their instances. The premises of my argument are intuitive claims about resemblances among some properties that Lewis held on Humean grounds. (shrink)

I present an internal problem for David Lewis’s genuine modal realism. My aim is to show that his analysis of modality is inconsistent with his metaphysics. I consider several ways of modifying the Lewisian analysis of modality, but argue that none are successful. I argue that the problem also affects theories related to genuine modal realism, including the stage theory of persistence and modal fictionalism.

The standard conception of God is that of a necessary being. On a possible worlds semantics, this entails that God exists at every possible world. According to the modal realist account of David Lewis, possible worlds are understood to be real, concrete worlds—no different in kind from the actual world. Some have argued that Lewis’s view is incompatible with classical theism (e.g., Sheehy, 2006). More recently, Ross Cameron (2009) has defended the thesis that Lewisian modal realism and classical theism are (...) in fact compatible. I argue that this is not the case. Modal realism, I argue, is equipped to accommodate necessary beings in only one of three ways: (1) By way of counterpart theory, or (2) by way of a special case of trans-world identity for causally inert necessary beings (e.g., pure sets), or else (3) causally potent ones which lack accidental intrinsic properties. However, each of these three options entails unacceptable consequences—(1) and (2) are incompatible with theism, and (3) is incompatible with modal realism. I conclude that (at least) one of these views is false. (shrink)

In this article, I am interested in four versions of what is often referred to as "the Humphrey objection". This objection was initially raised by Kripke against Lewis's modal counterpart theory, so this is where I will start the discussion. As we will see, there is a perfectly good answer to the objection. I will then examine other places where a similar objection can be raised: it can arise in the case of temporal counterpart theory (in fact, it can arise (...) in the case of all kinds of counterpart theories, independently on modal realism), and a very similar worry can also arise against modal realism itself or against an ersatzist theory of possible worlds itself. For similar reasons, in similar situations, a similar objection will arise. What is interesting is that it is not the case that a similar response can be given in all of these similar cases. So, in the end, we will see what dissimilarities there are and how and why they are relevant. In particular, we will see the differences there are between alethic modalities and temporal modalities. In the case of alethic modalities (metaphysical necessity and possibility), the objection can be answered by appealing to the notion of representation, while this does not work very well in the case of temporal modalities. (shrink)

According to the Truthmaker Principle: every truth has a truthmaker. Attempts to come to grips with the Truthmaker Principle played a prominent role in Lewis’s metaphysical writings over the last fifteen years of his career. Although Lewis agreed that the truth of propositions must somehow be ontologically grounded, the Truthmaker Principle was too strong: it conflicted with two of Lewis’s most fundamental metaphysical assumptions, the uniqueness of composition and the Humean denial of necessary connections. Lewis endorsed instead a weaker principle: (...) Truth Supervenes on Being. But towards the end of his career, he changed course, noting that his critique of the Truthmaker Principle rested on essentialist assumptions that he, as a counterpart theorist, does not accept. Once freed from those assumptions, a counterpart theorist can accept the Truthmaker Principle after all without buying into unmereological composition and mysterious necessary connections. (shrink)

This chapter is concerned with the coextension difficulty for nominalist theories of properties that reject tropes alongside universals. After carefully explaining the coextension difficulty and describing the theories it targets, the chapter describes different solutions to the difficulty. These solutions differ with respect to how much involved they are into a dualist approach to coextension. A dualist approach to a case of coextension consists in agreeing with the realist that the relevant ascriptions of properties are numerically distinct. A monist approach (...) to a case of coextension consists in contending that the relevant ascriptions of properties are identical. In this chapter, I defend a monist approach to cases of coextension that appeals to a counterpart theory for propositions. (shrink)

David Lewis holds that a single possible world can provide more than one way things could be. But what are possible worlds good for if they come apart from ways things could be? We can make sense of this if we go in for a metaphysical understanding of what the world is. The world does not include everything that is the case—only the genuine facts. Understood this way, Lewis's “cheap haecceitism” amounts to a kind of metaphysical anti-haecceitism: it says there (...) aren't any genuine facts about individuals over and above their qualitative roles. (shrink)

Actualist counterpart theory replaces David Lewis’s concrete possible worlds and individuals with ersatz worlds and individuals, but retains counterpart theory about de re modality. While intuitively attractive, this view has been rejected for two main reasons: the problem of indiscernibles and the Humphrey objection. I argue that in insisting that ersatz individuals play the same role as Lewisian individuals, actualists commit the particularist fallacy. The actualist should not require stand-ins for every Lewisian individual. Ersatz individuals should instead be construed as (...) representations of actually existing qualitative ways for individuals to be, or qualitative properties individuals can instantiate. This necessitates changes elsewhere. Non-instrumental uses of Kripke semantics and standard counterpart semantics also require stand-ins for particular non-actual individuals. I argue that the actualist should instead adopt a non-standard counterpart semantics that more clearly illuminates the role that actual properties and relations play in explaining de re possibilities and necessities. The result is an intuitive and forceful reply to both the problem of indiscernibles and the Humphrey objection. (shrink)

This paper presents and motivates a counterpart theoretic semantics for quantifi ed modal logic based on a fleshed out account of Lewis's notion of a `possibility.' According to the account a possibility consists of a world and some haecceitistic information about how each possible individual gets represented de re. A semantics for quanti ed modal logic based on evaluating formulae at possibilities is developed. It is shown that this framework naturally accommodates an actuality operator, addressing recent objections to counterpart theory, (...) and is equivalent to the more familiar Kripke semantics for quanti fied modal logic with an actuality operator. (shrink)

It is a commonsense thesis that unactualized possibilities are not parts of actuality. To keep his modal realism in line with this thesis, David Lewis employed his indexical account of the term “actual.” I argue that the addition of counterpart theory to Lewis’s modal realism undermines his strategy for respecting the commonsense thesis. The case made here also reveals a problem for Lewis’s attempt to avoid haecceitism.

I call anti-resemblism the thesis that independently of any contextual specification there is no determinate fact of the matter about the comparative overall similarity of things. Anti-resemblism plays crucial roles in the philosophy of David Lewis. For instance, Lewis has argued that his counterpart theory is anti-essentialist on the grounds that counterpart relations are relations of comparative overall similarity and that anti-resemblism is true. After Lewis committed himself to a form of realism about natural properties he maintained that anti-resemblism is (...) true about the relations of overall similarity that enter his counterpart theory and his analysis of counterfactuals. However, in this article I argue that Lewis’s account of degrees of naturalness for properties combined with his modal realism entails that anti-resemblism is false. The Lewisian must amend Lewis’s system if she aims to benefit from the alleged virtues of anti-resemblism. I consider two ways of amending it, neither of which is a free lunch. (shrink)

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures.

Counterpart theory is often advertised by its track record at solving metaphysical puzzles. Here I focus on puzzles of occasional identity, wherein distinct individuals at one world or time appear to be identical at another world or time. To solve these puzzles, the usual interpretation rules of counterpart theory must be extended beyond the simple language of quantified modal logic. I present a more comprehensive semantics that allows talking about specific times and worlds, that takes into account the multiplicity and (...) sortal-dependence of counterpart relations, and that does not require names to denote actual or present individuals. In addition, the semantics I defend does not identify ordinary individuals with world-bound or time-bound stages and thereby avoids the most controversial aspect of counterpart theory. Humphrey’s counterpart at other worlds or times is none other than Humphrey himself. (shrink)

This is a supplement to our book "Le tribolazioni del filosofare. Comedia metaphysica ne la quale si tratta de li errori & de le pene de l’Infero". It features an entirely new canto of the poem (originally thought to be lost) along with an extensive commentary. The canto covers the first ring of the circle of the Sullen, which hosts the Adverse to the Possible, and deals with several philosophical questions concerning the metaphysics of modality.

Surely, it is possible that you believe falsely about this-or-that modal matter. In light of the various ways the world could be arranged, it is plausible thatthere is a nearby possible world, which would be almost identical to the actual world, if it were actualized, where you and your modal counterpart disagree over modal belief p. You might be tempted to think that your modal belief is true, while hers is not. It is not clear why this is so; after (...) all, you would each have the same evidence, cognitive abilities etc., if you were both actualized. This point generalizes to all of your modal beliefs, this seems to strongly imply that the probability that you have true modal beliefs appears inscrutable. Thus, you have some reason to withhold belief, on modal matters. (shrink)

One popular theodicy says that good can’t exist without evil, and so God must allow evil in order to allow good. Call this the counterpart theodicy. The counterpart theodicy relies on a metaphysical claim about existence—good cannot exist without evil. A second popular theodicy says that we would be unable to know/recognize/appreciate the good without evil, and so God is forced to allow evil in order to allow for such appreciation. Call this the appreciation theodicy. The appreciation theodicy relies on (...) an epistemological claim about recognition or appreciation—we are unable to know/recognize/appreciate good without evil (even if it is possible for good to exist without evil). Determining whether either of these theodicies is a success requires a careful discussion of whether either meets the conditions on a successful theodicy. I argue that both fail. (shrink)

Fara and Williamson (Mind, 2005) argue that counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.

The counterpart theorist has a problem: there is no obvious way to understand talk about actuality in terms of counterparts. Fara and Williamson have charged that this obstacle cannot be overcome. Here I defend the counterpart theorist by offering systematic interpretations of a quantified modal language that includes an actuality operator. Centrally, I disentangle the counterpart relation from a related notion, a ‘representation relation’. The relation of possible things to the actual things they represent is variable, and an adequate account (...) of modal language must keep track of the way it is systematically shifted by modal operators. I apply my account to resolve several puzzles about counterparts and actuality. In technical appendices, I prove some important logical results about this ‘representational’ counterpart system and its relationship to other modal systems. (shrink)

It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are (...) adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis' counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics. (shrink)

In recent work, Jonathan Schaffer (Mind 119: 341–376, 2010) has attempted to argue that counterpart theorists are committed to holding that any two actual objects are bound together in a modally substantial sense. By clarifying the core elements of counterpart theory, I explain why Schaffer’s argument fails.

In this paper, I examine the putative incompatibility of three theses: (1) Haecceitism, according to which some maximal possibilities differ solely in terms of the non-qualitative or de re possibilities they include; (2) Modal correspondence, according to which each maximal possibility is identical with a unique possible world; (3) Counterpart theory, according to which de re modality is analyzed in terms of counterpart relations between individuals. After showing how the modal realism defended by David Lewis resolves this incompatibility by rejecting (...) modal correspondence, I defend modal correspondence and develop an alternative strategy for reconciling these theses. Specifically, I examine Lewis’s arguments against non-qualitative counterpart theory and undermine them by developing a novel version of non-qualitative counterpart theory that appeals to a metaphysics of bare particulars. I then indicate how this version of non-qualitative counterpart theory accommodates both haecceitism and modal correspondence. (shrink)

This paper is an informal presentation of the ideas presented formally in ”Relative-Sameness Counterpart Theory”. Relative-sameness relations -- such as being the same person as -- are like David Lewis’s “counterpart” relations in the following respects: (i) they may hold over time or across worlds between objects that aren’t cross-time or cross-world identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different contexts. They differ from his counterpart relations, however, (...) in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis’s Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). The use of sameness as opposed to similarity relations in the analysis of de-re temporal and modal predication renders the resulting truth conditions as statable in terms that proponents of Kripke’s identity-based analysis can accept. (shrink)